$(-30i)+(52-30i)=$ Express your answer in the form $(a+bi)$.
Solution: Background Complex numbers can be added or subtracted by separately adding or subtracting their real and imaginary terms. To add or subtract complex numbers: Expand parentheses (attending to minus signs outside of parentheses if necessary) Combine all real terms (terms that do not contain $i$ ), and add or subtract them. Combine all imaginary terms (terms that contain $i$ ), and add or subtract them. Combining Like Terms $\begin{aligned} ({-30}i)+({52}{-30}i)&={-30}i+{52}{-30}i \\\\ &={52}{-30}i{-30}i \\\\ &={52}{-60}i \end{aligned}$ Summary $({-30}i)+({52}{-30}i)={52}{-60}i$